Question

What is the cost of a packet of bread if 6 packets of bread and 3 packets of butter together cost Rs 90 and a packet of butter costs thrice that of a packet of bread?

Answer 1

Hint: We will denote the cost of a packet of bread and the cost of a packet of butter as variables. Then we will express the given information in the form of linear equations. Finally, we will solve the two linear equations to get the cost of a packet of bread.

Complete step-by-step answer:
Let the cost of a packet of bread be Rs \[x\] and the cost of a packet of butter be Rs \[y\].
It is given that the total cost of 6 packets of bread and 3 packets of butter is Rs 90.
The cost of 6 packets of bread is Rs \[6x\] and the cost of 3 packets of butter is Rs \[3y\]. The total cost is Rs 90. Thus, we have
\[6x + 3y = 90\] ………..\[\left( 1 \right)\]
Also, it is given that the cost of a packet of butter is thrice the cost of a packet of bread. i.e., \[y\] is equal to 3 times \[x\]. Hence,
\[y = 3x\] ………..\[\left( 2 \right)\]
We will substitute equation \[\left( 2 \right)\] in equation \[\left( 1 \right)\]. This gives us
\[6x + 3\left( {3x} \right) = 90\]
Multiplying 3 by \[3x\], we get
\[ \Rightarrow 6x + 9x = 90\]
Adding like terms on the LHS, we get
\[ \Rightarrow 15x = 90\]
Now, dividing both sides by 15, we have
\[ \Rightarrow \dfrac{{15x}}{{15}} = \dfrac{{90}}{{15}}\]
\[ \Rightarrow x = 6\]
Therefore, the cost of a packet of bread is Rs 6.

Note : We can also make the substitution as follows:
From equation \[\left( 2 \right)\], \[x = \dfrac{y}{3}\].
Substituting \[x = \dfrac{y}{3}\] in equation \[\left( 1 \right)\], we get
\[6\left( {\dfrac{y}{3}} \right) + 3y = 90\]
Simplifying the expression, we get
\[ \Rightarrow 2y + 3y = 90\]
Adding the like terms, we get
\[ \Rightarrow 5y = 90\]
Dividing both sides by 5, we get
\[ \Rightarrow y = 18\]
Now substituting \[y = 18\] in equation \[\left( 3 \right)\], we get
\[\begin{array}{l}18 = 3x\\ \Rightarrow x = 6\end{array}\]